How do you find the average value of a function over a region thatis expressed in polar coordinates?

Q: How can you sometimes find the area bounded by a parametrized curve and one of the coordinate axes?

A: Let the equation of parametrized curve be

Q: Sketch the region enclosed by the curves and find its area. y = x, y=3x, y= -x + 2 AREA =

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Q: Sketch the region enclosed by the curves y = x| and y = x2 2. Decide whether to integrate with…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Recall: If x=f(y) and x=g(y) are two continuous function on [a,b] and f(y)≥g(y) on a≤y≤b , then the…

Q: Sketch the region enclosed by a y²-56 and x+y=0 Decide whether to integrate with respect to x or y,…

A: Consider the curves  x+y2=56x+y=0

Q: Find the area of a region bounded above by the curve y = x' and below by y = 0 over the interval [0,…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by y = 2x and y = 3x. Decide whether to integrate with respect to r or y.…

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Q: Sketch the region enclosed by x + y² = 30 and x + y = 0. Decide whether to integrate with respect to…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: The sketch below shows the area enclosed between the curves.

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to xx or…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by x + y x + y = 0. Decide whether to integrate with 6 and respect to x…

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Q: Find the area of the region enclosed by the curves y = x² and y = 5x by integrating with respect to…

A: To find The area of the region enclosed by the curves y=x^2 and y=5x by integrating with respect to…

Q: Sketch the region enclosed by a+ y = 30 and +y = 0. Decide whether to integrate with respect to x or…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect tox or y.…

A: Topic: integration

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Refer to the figure shown below:   The (grey) bounded region lies within the two given curves which…

Q: Find the centroid of the area bounded by the curves y = x^3, x = 0 and y = 8

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Q: Graph the region bounded by the curves y =x, y=. Find the centroid of the region.

A: Given that y=x2 and y=x re-write the above curve as, let fx=x2 and gx=x The graph of these two…

Q: Sketch the region enclosed by x+y2=42 and x+y=0. Decide whether to integrate with respect to x or y.…

A: The given curves are x+y2=42 and x+y=0 We have to sketch the region enclosed by these two curves and…

Q: Sketch the region enclose by the given curves. Decide whether to integrate with respect to x or y.…

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Q: True or false? When the region between two graphs is rotated about the x-axis, the cross sections of…

A: Assume the two graphs is given as

Q: Find the area of the region between the curves y = æ and y = Va. Area between curves

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Q: 16. y= Vx, y= %3D

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Q: Find the centroid of the area under y = 4 – x^2 in the first quadrant.

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Determine the area of the given region under the curve. 1 y = y

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by the curves and find its area. y = x, y = 2x, y= -x + 4 AREA =

A: The region is bounded by y=x, y=2x, y=-x+4

Q: Sketch the region enclosed by a + y² = 6 and æ + y = 0. Decide whether to integrate with respect to…

A: In the above figure, area enclosed by the curves x+y2=6 and x+y=0 is given.

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: We have to find the area of this region

Q: x- sin x+y) dA

A: The given problem is to evaluate the given double integral over the given region R enclosed by the…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: The given curves equations are     2y=4xy=32y+2x=6

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y…

A: Let's find area enclosed by given  curves.

Q: Sketch the region enclosed by a + y = 6 and æ + y= 0. Decide whether to integrate with respect to a…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Here given curves 2y=3x, y=5 and 2y+1x=4 or y=32x⇒x=23y2And y=5 and  2y+x=4⇒x=4-2y

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Follow the procedure given below.

Q: Find the moment of inertia of the area bounded by the curve y^2 = 4x, the line x = 1, the x-axis on…

A: Given: The area bounded by the curve y2=4x, the line x=1, the x-axis on the first quadrant with…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: The graph is shown below:

Q: Sketch the region bounded by lines x= 0, y=0, x=16, and curve y=Vx . Then find the enclosed area of…

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Q: Find the average value of r over the solid sphere ρ ≤ a (spherical coordinates).

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: NOTE: Refresh your page if you can't see any equations. . the first function is  . the second…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: The given curves are  y =3 2y = 4x 2y + x = 5 Intersection points of both curves are  5 - x = 4x…

Q: Sketch the region enclosed by a + y = 30 and r + y = 0. Decide whether to integrate with respect to…

A: Recall: If f(y) and g(y) are continuous on a,b and f(y)≥g(y)  on a≤y≤b , then the area of the region…

Q: Find the area of the region bounded by the given curves. Decide whether to integrate with respect…

A: Given query is to find the are of the region bounded by the curve.

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Find the centroid of the area in the first quadrant under the curve y = 4 − x 2.

A: We have to find the centroid of the area in the first quadrant under the curve y=4-x2.

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.